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X-WR-CALNAME:Analysis and Its Applications Seminar
X-WR-CALDESC:Analysis and Its Applications Seminar Calendar, University of 
 Arizona Program in Applied Mathematics
X-WR-TIMEZONE:US/Arizona
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TZID:US/Arizona
BEGIN:STANDARD
DTSTART:19700101T000000
TZOFFSETFROM:-0700
TZOFFSETTO:-0700
TZNAME:MST
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BEGIN:VEVENT
CATEGORIES:Analysis & Its Applications
DESCRIPTION:After reviewing some more examples of topological groupoids\, I
  will present the notion of groupoid action on a topological space. This c
 an then be generalized to groupoid actions on C*-algebras. I will end up w
 ith a discussion of the tangent groupoid\, its associated C*-algebra\, and
  their use in index theory.
DTSTAMP:20080424T153416Z
DTSTART;TZID=US/Arizona:20080422T123000
DURATION:PT1H
LOCATION:Math 402
SUMMARY:Dorin Dumitrascu: Groupoid Actions on C*-algebras\, Part II
UID:20080424T173416CEST-mVwRb5vObc@appliedmath.arizona.edu
END:VEVENT
BEGIN:VEVENT
CATEGORIES:Analysis & Its Applications
DESCRIPTION:The main goal of the talk is to discuss the notion of groupoid 
 action on a C*-algebra and point out some of the difficulties that one has
  to deal with. I will use two examples to show the usefulness of groupoids
 . The first is the characterization of an AF algebra as the C*-algebra of 
 a principal groupoid\, and the second is the use of the tangent groupoid i
 n index theory.
DTSTAMP:20080424T153416Z
DTSTART;TZID=US/Arizona:20080415T123000
DURATION:PT1H
LOCATION:Math 402
SUMMARY:Dorin Dumitrascu: Groupoid Actions on C*-algebras
UID:20080424T173416CEST-DE0s117xuX@appliedmath.arizona.edu
END:VEVENT
BEGIN:VEVENT
CATEGORIES:Analysis & Its Applications
DESCRIPTION:One of the commonly used equations describing nematic liquid cr
 ystals is the so-called Doi-Smoluchowski equation. In essence\, it is a ki
 netic equation for evolution of the orientation probability density of the
  system. I will present an analogue of this equation for spatially inhomog
 eneous systems and will discuss the associated problems of moment closure 
 and reduction to Ginzburg-Landau type dynamics.
DTSTAMP:20080424T153416Z
DTSTART;TZID=US/Arizona:20080408T123000
DURATION:PT1H
LOCATION:Math 402
SUMMARY:Ibrahim Fatkullin: Diffusive Transport in Nematics
UID:20080424T173416CEST-zvUN6wnVn3@appliedmath.arizona.edu
END:VEVENT
BEGIN:VEVENT
CATEGORIES:Analysis & Its Applications
DESCRIPTION:I will talk about the regularity properties of the free boundar
 y for the Stefan problem\, which models the phase transition between solid
 s and liquids\, and will present a recent work: If the initial free bounda
 ry is Lipschitz with a small Lipschitz constant\, then the weak (viscosity
 ) solution of the one-phase Stefan problem immediately regularizes and is 
 smooth in space and time\, for a small positive time.
DTSTAMP:20080424T153416Z
DTSTART;TZID=US/Arizona:20080401T123000
DURATION:PT1H
LOCATION:Math 402
SUMMARY:Sunhi Choi: Free Boundary Regularity for the Stefan Problem
UID:20080424T173416CEST-7OEvsrBVvx@appliedmath.arizona.edu
END:VEVENT
BEGIN:VEVENT
CATEGORIES:Analysis & Its Applications
DESCRIPTION:I will start with examples of models that describe collective b
 ehaviors in animal herds\, fish schools\, and bird flocks\, and explain ho
 w some of these ideas can be extended to describe the dynamics of bacteria
 l systems which do not communicate with one another. This will take us to 
 problems related to the dynamics of gases\, such as for instance granular 
 gases. In that context\, I will show simulations that explore the question
  of how the macroscopic behavior of a system of interacting particles can 
 be affected by changing the collision rules between these particles. I wil
 l then explain how I think this could be related to the Lyapunov modes of 
 the dynamics of the system. The structure of these modes has been widely s
 tudied in the literature and\, in particular\, the modes associated with s
 mall (in absolute value) Lyapunov exponents are known to have large-scale 
 correlations. I will summarize the contents of a paper by Eckmann and Gat 
 (J. Stat. Phys.\, 2000)\, which tries to explain this phenomenon by lookin
 g at the eigenvectors of a random matrix.\n
DTSTAMP:20080424T153416Z
DTSTART;TZID=US/Arizona:20080325T123000
DURATION:PT1H
LOCATION:Math 402
SUMMARY:Joceline Lega: Collective Behaviors\, Lyapunov Modes\, and Random M
 atrices
UID:20080424T173416CEST-xzeJttF4vR@appliedmath.arizona.edu
END:VEVENT
BEGIN:VEVENT
CATEGORIES:Analysis & Its Applications
DESCRIPTION:In this talk I hope to explain the Deift-Zhou steepest descent 
 method for oscillatory Riemann-Hilbert problems (RHPs)\, which can be thou
 ght of as a method analogous to the steepest descent method for obtaining 
 asymptotic limits of integral expressions. The asymptotic limits I will co
 nsider come from RHPs associated with the nonlinear Schrodinger equation.\
 n
DTSTAMP:20080424T153416Z
DTSTART;TZID=US/Arizona:20080311T123000
DURATION:PT1H
LOCATION:Math 402
SUMMARY:Robert Jenkins: An Asymptotic Method for Riemann-Hilbert Problems
UID:20080424T173416CEST-pn7usBVb0Z@appliedmath.arizona.edu
END:VEVENT
BEGIN:VEVENT
CATEGORIES:Analysis & Its Applications
DESCRIPTION:Concentration inequalities provide effective tools in probabili
 stic contexts to deal with deviations of random variables from their expec
 tations. We will give an introduction to concentration inequalities in a c
 ontext that has applications\, or potential applications\, to questions in
  random matrix theory.
DTSTAMP:20080424T153416Z
DTSTART;TZID=US/Arizona:20080304T123000
DURATION:PT1H
LOCATION:Math 402
SUMMARY:Nick Ercolani: Applications of Concentration Inequalities
UID:20080424T173416CEST-9iUaChAvja@appliedmath.arizona.edu
END:VEVENT
BEGIN:VEVENT
CATEGORIES:Analysis & Its Applications
DESCRIPTION:Gradient flows ostensibly have dynamics that (1) result from th
 e decrease of energy and (2) do not exhibit oscillations. Neither of these
  statements is true for limits of singularly perturbed systems\, however. 
 This talk illustrates these points in the context of liquid film evolution
 . \n\nEnergy-driven coarsening processes arise as the late-stage dynamics 
 of many problems. Two examples are the spinodal decomposition of binary mi
 xtures and the dewetting of an unstable film of viscous liquid. The first 
 case gives rise to Ostwald ripening\, where large particles grow at the ex
 pense of smaller ones by exchanging material. Migration of the particles a
 s a result of the ambient mass flux is a slower process and is usually ign
 ored.  In contrast\, the nearly singular kinetics associated with the hydr
 odynamics of liquid films makes the role of migration significant. We disc
 uss this phenomenon from both a variational and a perturbation theory poin
 t of view. \n\nThe effects of gravity or hoop stress can also lead to migr
 ation\, but for different reasons. Interaction of droplets or fluid ridges
  is shown to give rise to a system which produces neighbor-neighbor repuls
 ion and oscillatory dynamics.\n
DTSTAMP:20080424T153416Z
DTSTART;TZID=US/Arizona:20080226T123000
DURATION:PT1H
LOCATION:Math 402
SUMMARY:Karl Glasner: Migration Phenomena of Liquid Film Droplets and Surpr
 ises about Singularly Perturbed Gradient Flows
UID:20080424T173416CEST-JH186ulBRs@appliedmath.arizona.edu
END:VEVENT
BEGIN:VEVENT
CATEGORIES:Analysis & Its Applications
DESCRIPTION:For the eigenvalues of a Schroedinger operator with a nonnegati
 ve potential\, Dolbeault\, Felmer\, Loss\, and Paturel proved (JFA\, 2006)
  a class of inequalities of Lieb-Thirring type relating functions of the s
 pectrum to (appropriate) integrals which depend on the potential. These in
 equalities include in particular the classical Golden-Thompson (also calle
 d Kac-Ray) inequality and a gamut of new inequalities for the spectral zet
 a function and other functions. \n\nIn this work\, we use the Bethe sum ru
 le and transform methods to prove a parallel set of inequalities for the e
 igenvalues of the fixed membrane problem. We also prove the equivalence of
  the Berezin-Li-Yau inequality with a classical inequality of Kac\, analyz
 e the work of A. Melas in a new light\, and propose new conjectures. \n\nT
 his is joint work with Professor Evans Harrell of Georgia Tech. \n\nA prep
 rint is available at http://arxiv.org/abs/0712.4088\n
DTSTAMP:20080424T153416Z
DTSTART;TZID=US/Arizona:20080212T123000
DURATION:PT1H
LOCATION:Math 402
SUMMARY:Lotfi Hermi: A Class of New Inequalities for the Eigenvalues of the
  Dirichlet Laplacian
UID:20080424T173416CEST-DK6iUJzn1g@appliedmath.arizona.edu
END:VEVENT
BEGIN:VEVENT
CATEGORIES:Analysis & Its Applications
DESCRIPTION:I will describe some open questions in the asymptotic analysis 
 of Riemann-Hilbert problems\, random matrices\, and integrable PDEs.
DTSTAMP:20080424T153416Z
DTSTART;TZID=US/Arizona:20080205T123000
DURATION:PT1H
LOCATION:Math 402
SUMMARY:Ken McLaughlin: A few open directions for research in random matric
 es\, integrable PDEs\, and Riemann-Hilbert problems
UID:20080424T173416CEST-OWVCwpTNXV@appliedmath.arizona.edu
END:VEVENT
BEGIN:VEVENT
CATEGORIES:Analysis & Its Applications
DESCRIPTION:Thin elastic sheets are very common in both natural and man-mad
 e structures. The configurations these structures assume in space are ofte
 n very complex and may contain many length scales\, even in the case of un
 constrained thin sheets. We will show evidence of the simplicity of the in
 trinsic geometry leading to these complex three-dimensional configurations
 \, and discuss the mechanism of shaping thin elastic sheets through the pr
 escription of intrinsic metric.\n\nCurrent reduced (two-dimensional) elast
 ic theories devised to describe thin structures treat either plates (flat 
 bodies having no structure along their thin dimension) or shells (non-flat
  bodies having a non-trivial structure along their thin dimension). We pro
 pose the concept of non-Euclidean plates\, which are neither plates nor sh
 ells\, to approximate many naturally formed thin elastic structures. We de
 rive a thin plate theory which is a generalization of existing linear plat
 e theories for large displacements but small strains\, and arbitrary intri
 nsic geometry. We conclude by surveying some experimental results for labo
 ratory-engineered non-Euclidean plates.
DTSTAMP:20080424T153416Z
DTSTART;TZID=US/Arizona:20080129T123000
DURATION:PT1H
LOCATION:Math 402
SUMMARY:Efi Efrati: Elastic Theory of Non-Euclidean Plates
UID:20080424T173416CEST-A0MZUh6v7u@appliedmath.arizona.edu
END:VEVENT
BEGIN:VEVENT
CATEGORIES:Analysis & Its Applications
DTSTAMP:20080424T153416Z
DTSTART;TZID=US/Arizona:20080122T123000
DURATION:PT1H
LOCATION:Math 402
SUMMARY:Organizational meeting
UID:20080424T173416CEST-ARzIK4sZae@appliedmath.arizona.edu
END:VEVENT
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